91Ó°ÊÓ

Apply the quotient rule for exponents, if possible, and write each result using only positive exponents. Assume that all variables represent nonzero real numbers. $$ \frac{6^{4}}{6^{-2}} $$

Let \(f(x)=x^{2}-9, g(x)=2 x,\) and \(h(x)=x-3 .\) Find each of the following. $$ \left(\frac{h}{g}\right)\left(-\frac{1}{2}\right) $$

The factors in the following exercises involve fractions or decimals. Apply the methods of this section, and find each product. $$ \left(3 w+\frac{1}{4} z\right)(w-2 z) $$

Let \(f(x)=x^{2}+4, g(x)=2 x+3,\) and \(h(x)=x-5 .\) Find each of the following. \((h \circ g)(x)\)

Let \(f(x)=x^{2}-9, g(x)=2 x,\) and \(h(x)=x-3 .\) Find each of the following. $$ \left(\frac{h}{g}\right)\left(-\frac{3}{2}\right) $$

Apply the quotient rule for exponents, if possible, and write each result using only positive exponents. Assume that all variables represent nonzero real numbers. $$ \frac{7^{5}}{7^{-3}} $$

The factors in the following exercises involve fractions or decimals. Apply the methods of this section, and find each product. $$ \left(5 r+\frac{2}{3} y\right)(r-5 y) $$

Let \(f(x)=x^{2}+4, g(x)=2 x+3,\) and \(h(x)=x-5 .\) Find each of the following. \((h \circ f)(x)\)

Find each product. $$ [(5 x+1)+6 y]^{2} $$

Apply the quotient rule for exponents, if possible, and write each result using only positive exponents. Assume that all variables represent nonzero real numbers. $$ \frac{6^{-3}}{6^{7}} $$